Squid Game -- Marbles Scene

In game 4/episode 6 of Squid Game, players are made to form teams of two, however they like.

After 19 teams were formed, they let the odd 39th player advance to the next round automatically.

Then each player was given ten marbles. They were told to play anything against their teammate. The goal was to attain all 20 marbles, between the two members, without the use of force. Cheating was permitted, but let's not get into that.

Most players chose to play a game with the following rules:

1. Players took turns as what I will call the Hider and the Guesser.
2. The Hider would hide any number of his marbles, between one and his total marbles, in his hand.
3. The Guesser would make a wager, as indicated by a hidden number of marbles in his hand. This wager must be at least one and no more than the number of Marbles possessed by the Hider. For example, if the Hider has 7 and the Guesser has 13, the Guesser would bet 1 to 7 marbles.
4. The Guesser guesses whether the Hider is hiding an Odd or Even number of marbles.
5. The Hider opens his hand, revealing the parity (odd/even) of the number of hidden marbles.
6. The Guesser opens his hand, revealing his bet.
7. If the Guesser correctly guessed, the Hider gives him the number of marbles indicated by his bet. Otherwise, if the Guesser was incorrect, he gives to the Hider the number of marbles of his bet.

This continues, with the players alternating between Hider and Guesser, until one player has all 20 marbles. The loser is then immediately "eliminated," with a bullet through his head.

There is some discussion about the strategy of this game on other sites, but most of them get the rules wrong. The rules to this Marbles game are only briefly explained in the 0:44 point in the dubbed video below. However, every instance of the game is consistent with the rules as I just explained them.


Direct: https://youtu.be/NyLX0ufVg00?t=44

The question at hand is what is the optimal strategy for this game, assuming both players are perfect logicians? It is easy to say if you and the Guesser and have m marbles, where m<=10, then don't wager m-1. That would leave one marble if wrong. You then must hide one marble on the next turn, which would be obvious for your opponent to predict.

I personally think no strategy is superior to betting min(m,20-m), where m is the Guessers number of marbles. It may be that all strategies are equally good, as long as you don't bet m-1.

The question for the poll is which was your favorite game of the show?

Link: best strategies for 'Squid Game' episode 6 game 4 "marble game" players

I believe you have a typo in roll number six. The initial ‘if’ does not belong.

I’m also not entirely sure of how this works. Is the guesser guessing a number of marbles, or just whether it’s odd or even? And is it indicated by the number of marbles in his hand or verbal?

——

Loved the show, but for the record, I still don’t understand the rules of ‘Squid’ game.

Quote: DJTeddyBear

I believe you have a typo in roll number six. The initial ‘if’ does not belong.

Thanks.

Quote:

I’m also not entirely sure of how this works. Is the guesser guessing a number of marbles, or just whether it’s odd or even? And is it indicated by the number of marbles in his hand or verbal?

Odd or even -- by the number of marbles in the hand of the Hider.

Quote:

Loved the show, but for the record, I still don’t understand the rules of ‘Squid’ game.
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Neither do I. I've asked Korean friends about it, but didn't get very far, not knowing the Korean term for the game and my friends never watched the show.

I thought I clicked the easy math problem thread for a second lol